Palm Beach County, Florida Jupiter-Carlin Segment Section 934 Report. Appendix A Engineering Appendix

Transcription

1 Palm Beach County, Florida Jupiter-Carlin Segment Section 934 Report Appendix A Engineering Appendix

2 Table of Contents 1 Background Purpose Natural Forces Winds Waves Tides and Currents Storm Effects Storm Surge Sea Level Rise Relative Sea Level Rise Beach Responses to Sea Level Change Historical Shoreline Change Effects of Adjacent Features Jupiter Inlet Beach-fx Life-Cycle Shore Protection Project Evolution Model Background & Theory Meteorological Driving Forces Coastal Morphology Shoreline Storm Response Applied Shoreline Change Project Induced Shoreline Change Performance Post Storm Berm Recovery Economic Evaluation Management Measures Emergency Nourishment Planned Nourishment Nourishment Templates Beach-fx Project Design Alternatives Recommendation Design Criteria Project Length Project Baseline Berm Elevation Berm Widths Beach Slopes Project Volumes and Renourishment Interval References A-i

3 Table of Figures Figure A- 1. Project Site... 1 Figure A- 2. Location of WIS Station #63457 Relative to Project (Not to Scale)... 3 Figure A- 3. Wind Rose WIS Station Figure A- 4. Little and Great Bahama Banks... 5 Figure A- 5. Wave Rose WIS Station Figure A- 6. Historic storm tracks Hurricanes and Tropical Storms ( , 50 mile radius) Figure A- 7. Storm Surge Zones, North Palm Beach County, Florida (FDEM, 2010) Figure A- 8. Relative Sea Level Change, Jupiter-Carlin ( 13 Figure A- 9. Shoreline Recession vs Year Figure A- 10. Estimated Volume Lost Versus Year Figure A- 11. MHW Changes, Jupiter-Carlin Study Area Figure A- 12. Beach-fx Model Setup Representation Figure A- 13. Model Reaches Relative to FDEP R-monuments Figure A- 21. Projected 2018 and Eroded Idealized Profile: Model Reach JC Figure A- 22. Projected 2018 and Eroded Idealized Profile: Model Reach JC Figure A- 23. Projected 2018 and Eroded Idealized Profile: Model Reach JC Figure A- 24. Projected 2018 and Eroded Idealized Profile: Model Reach JC Figure A- 25. Projected 2018 and Eroded Idealized Profile: Model Reach JC Figure A- 26. Projected 2018 and Eroded Idealized Profile: Model Reach JC Figure A- 27. Projected 2018 and Eroded Idealized Profile: Model Reach JC Figure A- 28. Hurricane Frances and Jeanne Wave and Water Level Data for SBEACH Calibration Figure A- 29. Hurricane Floyd and Irene Wave and Water Level Data for SBEACH Verification Figure A- 30. SBEACH Calibration: Profile R Figure A- 31. SBEACH Verification: Profile R Figure A- 32. SBEACH Calibration: Profile R Figure A- 33. SBEACH Verification: Profile R Figure A- 34. SBEACH Calibration: Profile R Figure A- 35. SBEACH Verification: Profile R Figure A- 36. SBEACH Calibration: Profile R Figure A- 37. SBEACH Verification: Profile R Figure A- 38. SBEACH Calibration: Profile R Figure A- 39. SBEACH Verification: Profile R Figure A- 40. SBEACH Calibration: Profile R Figure A- 41. SBEACH Verification: Profile R Figure A- 42. SBEACH Calibration: Profile R Figure A- 43. SBEACH Verification: Profile R Figure A- 44. Target MHW Shoreline Change Rate Figure A- 45. Target MHW Shoreline Change and Applied Erosion Rates Figure A- 46. Deep water and Nearshore Wave Angles Figure A- 47. Absolute Difference between Measured and Predicted Annual Shoreline Change (K=0.2 to 0.6), Larson et al Figure A- 48. Average Absolute Difference between Measured and Predicted Annual Shoreline Change (K=0.2 to 0.6) Figure A- 49. Absolute Difference between Measured and Predicted Annual Shoreline Change (K=0.40 to 0.46), Larson et al A-ii

4 Figure A- 50. Average Absolute Difference between Measured and Predicted Annual Shoreline Change (K=0.40 to 0.46) Figure A- 51. Average Annual Shoreline Change Rate from Larson et al Table of Tables Table A- 1. Average Wind Conditions... 2 Table A- 2. Seasonal Wind Conditions... 4 Table A- 3. Average Wave Heights (1980 to 2012)... 6 Table A- 4. Seasonal Wave Conditions... 7 Table A- 5. Peak Wave Period Percent Occurrence... 8 Table A- 6. Tidal Datums... 8 Table A- 7. Storm Tide Elevations (FDOT Station 2504) Table A- 9. Mean High Water Shoreline Position Change Table A- 10. Dredging History (Average Annual) in the Vicinity of Jupiter Inlet Table A- 11. Model Reaches Table A- 12. Palm Beach County Beach-fx Storm Seasons Table A- 14. Dimensions of Idealized FWP Pre-Storm Representative Profiles (2018 Shoreline) Table A- 15. SBEACH Calibrated Beach Characteristic and Sediment Transport Parameters Table A- 16. Existing Jupiter Carlin Project Dimensions Table A- 17. Measured Average Annual Shoreline Change Table A- 18. Final Parameters for Determining Shoreline Change Table A- 19. Nourishment Templates Table A- 20. Beach-fx Berm Distance Triggers and Threshold Volumes Table A- 21. Project Baseline Relative to R-monument Table A- 22. Nourishment Template Variable Dune Widths Table A- 23. Beach-fx Project Volumes and Renourishment Interval: Authorized Project A-iii

5 1 Background The Jupiter-Carlin Segment of the Palm Beach County Coastal Storm Risk Management (CSRM) project consists of restoring approximately 1.1 miles of beach between Palm Beach County, Florida Department of Environmental Protection (FDEP) reference monument R-13 (Jupiter Inlet south jetty) and R-19 (Carlin Park) (Figure A- 1). The project, initially constructed in 1995, consists of a zero-foot authorized berm and approximately 513,000 cubic yards of advanced material over the 1.1 mile project length. The authorized fill restores the 1990 mean high water (MHW) shoreline and provides additional material to offset erosive losses for seven years between each subsequent renourishment. 2 Purpose The purpose of this report is to determine if a 15-year extension of Federal participation in the Jupiter- Carlin Segment of the Palm Beach County authorized project is economically justified. Initial project construction occurred in The additional 15 years would therefore allow for continued maintenance of the existing project through Figure A- 1. Project Site A-1

6 A Section 934 analysis (see the Main Report for a complete discussion of Section 934 guidance) is a twostep process that consists of: (1) identification of current benefits of the existing project to determine if continued maintenance is economically justified and is consistent with current policies and (2) a reanalysis of the existing beach nourishment alternative, varying the berm width and renourishment interval in order to maximize net economic benefits. 3 Natural Forces 3.1 Winds Local winds are the primary means of generating the small-amplitude, short period waves that are an important mechanism of sand transport along the Florida shoreline. Palm Beach County lies at about 26.9 degrees latitude, slightly north of the tropical trade wind zone. Winds in this region vary seasonally with prevailing winds ranging from the northeast though the southeast. The greatest velocities originate from the north-northeast quadrant in fall and winter months and from the eastsoutheast quadrant in the spring and summer. Wind data offshore of the project area is available from the USACE Wave Information Study (WIS) Program. WIS hindcast data are generated using the numerical hindcast model WISWAVE (Hubertz, 1992). WISWAVE is driven by wind fields overlaying a bathymetric grid. Model output includes significant wave height, peak and mean wave period, peak and mean wave direction, wind speed, and wind direction. In the Atlantic, the WIS hindcast database covers a 33-year period of record extending from 1980 to There are 523 WIS stations along the Atlantic Coast. WIS Station is representative of offshore deep water wind and wave conditions for the project area. Table A- 1 provides a summary of wind data from WIS Station 63457, located at latitude 26.92, longitude (about 9.5 miles east of Jupiter Beach; Figure A- 2). This table contains a summary of average wind speeds and frequency of occurrence broken down into eight 45 degree angle-bands. This table indicates that winds are predominantly from the east and southeast. The wind rose presented in Figure A- 3 provides a further breakdown of winds in the project area. Table A- 1. Average Wind Conditions Wind WIS Station #63457 ( ) Direction (from) Percentage Occurrence (%) Average Wind Speed (mph) North Northeast East Southeast South Southwest West Northwest A-2

7 Figure A- 2. Location of WIS Station #63457 Relative to Project (Not to Scale) Figure A- 3. Wind Rose WIS Station A-3

8 Wind conditions in Coastal Florida are seasonal. A further breakdown of the wind data provides a summary of the seasonal conditions (Table A- 2). Between December and March, frontal weather patterns driven by cold Arctic air masses can extend as far as South Florida. These fronts typically generate northeast winds before the frontal passage and northwest winds behind the front. This "Northeaster" behavior is responsible for the increased intensity of wind speed seen in the northeast sector winds during the fall and winter months. Northeasters may result in wave conditions that can cause extensive beach erosion and shorefront damage. The summer months (June through September) are characterized by southeast trade winds and tropical weather systems traveling west to northwest in the lower latitudes. Additionally, daily breezes onshore and offshore result from differential heating of land and water masses. These diurnal winds typically blow perpendicular to the shoreline and have less magnitude than trade winds and Northeasters. Daily breezes account for the general shift to east/southeast winds during the summer months when Northeasters no longer dominate. During the summer and fall months, tropical waves may develop into tropical storms and hurricanes, which can generate devastating winds, waves, and storm surge when they impact the project area. These storms contribute greatly to the overall longshore and cross-shore sediment transport at the site. These intense seasonal events will be discussed in greater detail under Section 3.4: Storm Effects. Table A- 2. Seasonal Wind Conditions WIS Station #63457 ( ) Month Average Wind Speed (mph) Predominant Direction (from) January 15.2 N February 15.0 E March 15.1 E April 13.8 E May 12.2 E June 10.8 E July 10.4 E August 10.5 E September 11.5 E October 14.0 NE November 15.5 NE December 15.2 E 3.2 Waves The energy dissipation that occurs as waves enter the nearshore zone and break is an important component of sediment transport in the project area. Incident waves, in combination with tides and storm surge, are important factors influencing the behavior of the shoreline. The Jupiter-Carlin study area is exposed to both short period wind-waves and longer period open-ocean swells originating predominantly from the northeast during spring, fall and winter months and from the northeast to southeast during summer months. A-4

9 Damage to the Jupiter-Carlin shoreline and upland development is attributable to large storm waves produced primarily by tropical disturbances, including hurricanes, during the summer months, and by Northeasters during the late fall and winter months. Because the study area is fully exposed to the open ocean in all seaward directions, the coastline is vulnerable to wave attack from distant storms as well as local storms. Most hurricanes and tropical storms traversing northward through the Atlantic within several hundred miles of the east coast are capable of producing large swells. These swell can propagate long distances, causing erosion along the Palm Beach County shoreline. Open-ocean swells originating from south of due east are blocked by two large shoals north and west of the Bahamas known as the Little Bahama Bank and the Great Bahama Bank, respectively (Figure A- 4). Water depths across the Bahama Banks average about 30 feet, so longer-period swells are reduced or eliminated by bottom friction or the presence of land masses as they traverse the Bank. During severe storm events such as hurricanes and tropical storms, high wind velocities can generate large, damaging waves over the relatively short distance between the Bahamas and Florida. Figure A- 4. Little and Great Bahama Banks Wave data for this report were obtained from the long-term USACE WIS hindcast database for the Atlantic coast of the U.S. This 33-year record extends from 1980 through 2012 and consists of a time- A-5

10 series of wave events at 3-hour intervals for stations located along the east and west coasts of the US as well as the Gulf of Mexico and Great Lakes. The WIS station closest to the project area is #63457, located 9.5 miles offshore. The location of WIS station #63457 relative to the study area is shown previously in Figure A- 2. Table A- 3 summarizes the percentage of occurrence and average wave height of the WIS waves by direction. It can be seen that the dominant wave direction is from northeast with contributions from the east and southeast. This can be seen in greater detail in the wave rose presented in Figure A- 5. The total wave climate reflects both the open-ocean swell and more locally generated wind-waves. Similar to wind conditions, wave conditions in Coastal Florida experience seasonal variability. The seasonal breakdown of wave heights shows that fall and winter months experience an increase in wave height due to Northeaster activity (Table A- 4). The intensity and direction of these fall/winter wave conditions are reflected in the dominant southward sediment transport and seasonal erosional patterns in the project area. In contrast, summer months experience milder conditions with smaller wave heights. Overall, waves originating from the east to northeast quadrant dominate. Wave periods have the same seasonality as wave heights. Table A- 5 provides a seasonal breakdown of percent occurrence by wave period. From this table, it can be seen that short period, locally-generated wind waves are common throughout the year, but dominate during the summer months. Shaded values show the dominant wave period for each month. During fall, winter and early spring months, higherenergy, longer-period storm waves are prevalent. The highest percentages of waves with period greater than 12.0 seconds occur during the winter and early spring when Northeasters are most common. 3.3 Tides and Currents Astronomical tides are created by the gravitational pull of the moon and sun and are entirely predictable in magnitude and timing. The National Oceanic and Atmospheric Administration (NOAA) regularly publishes tide tables for selected locations along the coastlines of the Unites States and selected locations around the world. These tables provide times of high and low tides, as well as predicted tidal amplitudes. Table A- 3. Average Wave Heights (1980 to 2012) Wave WIS Station #63457 ( ) Direction (from) Percentage Occurrence (%) Average Significant Wave Height (ft) North Northeast East Southeast South Southwest West Northwest A-6

11 Figure A- 5. Wave Rose WIS Station Table A- 4. Seasonal Wave Conditions WIS Station #63457 ( ) Month Average Wave Height (ft) Predominant Direction (from) January 3.9 NE February 3.9 NE March 4.0 NE April 3.4 NE May 2.9 NE June 1.9 NE-SE July 1.5 SE August 1.8 NE-SE September 2.9 NE October 4.2 NE November 4.5 NE December 4.1 NE A-7

12 Table A- 5. Peak Wave Period Percent Occurrence Tides in Palm Beach County are semidiurnal: two high tides and two low tides per tidal day. Tidal datums for the Jupiter-Carlin project site were determined using the NOAA VDatum model ( Tidal datums are summarized in Table A- 6. The tide range (difference between Mean High Water and Mean Low Water) is 2.81 feet in the project area. Table A- 6. Tidal Datums Tidal Datum Elevation Relative to NAVD88 (feet) Mean Higher High Water (MHHW) 0.45 Mean High Water (MHW) 0.24 North American Vertical Datum (NAVD88) 0.00 Mean Tide Level (MSL) Mean Low Water (MLW) Mean Lower Low Water (MLLW) The primary ocean current in the project area is the Florida Gulf Stream. With the exception of intermittent local reversals, it flows northward. The average annual current velocity is approximately 28 miles per day, varying from an average monthly low of 17 miles per day in November to an average monthly high of approximately 37 miles per day in July. The Gulf Streams lies approximately 10 to 15 miles offshore of the project area. The near-shore currents in the project vicinity are not generally influenced by the Gulf Stream, but may be influenced indirectly via interaction with incident waves. Littoral currents in addition to the presence of Jupiter Inlet affect the supply and distribution of sediment on the project shoreline. Longshore currents, induced by oblique wave energy, generally determine the long-term direction and magnitude of littoral transport. Cross-shore currents may have a more short term impact, but can result in both temporary and permanent erosion. The magnitude of these currents is determined by the wave characteristics, angle of waves from offshore, configuration of the beach, and the nearshore profile. For Palm Beach County beaches, the net sediment transport is from north to south. This is due to the dominant wave activity from the northeast during the fall and winter months, particularly northeaster storms. A-8

13 3.4 Storm Effects The shoreline of Palm Beach County is influenced by tropical systems during the summer and fall and by Northeasters during the late fall, winter, and spring. Although hurricanes typically generate larger waves and storm surge, Northeasters often have a greater impact on the shoreline because of their longer duration and higher frequency of occurrence. During intense storm activity, the shoreline is expected to naturally modify its beach profile. Storms erode and transport sediment from the beach into the active zone of storm waves. Once caught in the waves, this sediment is carried along the shore and re-deposited farther down the beach or is carried offshore and stored temporarily in submerged sand bars. Periodic and unpredictable hurricanes and coastal storms, with high energy breaking waves and elevated water levels, can change the width and elevation of beaches and accelerate erosion. After storms pass, lower energy waves usually return sediment from the sand bars to the beach, which is restored gradually to its natural shape. While the beach profile typically recovers from storm energy as described, extreme storm events may cause sediment to leave the beach system entirely, sweeping it into inlets or far offshore into deep water where waves cannot return it to the beach. Therefore, a portion of shoreline recession due to intense storms may never fully recover. Palm Beach County is located in an area of significant hurricane activity. Figure A- 6 shows historic tracks of hurricanes and tropical storms from 1858 to 2013, as recorded by the National Hurricane Center (NHC) and is available from the National Oceanic and Atmospheric Administration ( ). The shaded circle in the center of this figure indicates a 50-nautical mile radius drawn from the center of the study area and encompassing the entire Palm Beach County shoreline. Based on NHC records, 28 hurricanes and 30 tropical storms have passed within this 50-mile radius over the 156-year period of record. The 50-mile radius was chosen for display purposes in Figure A- 6 because any tropical disturbance passing within this distance, even a weak tropical storm, would be likely to produce some damage along the shoreline. Stronger storms are capable of producing significant damage to the coastline from far greater distances. In recent years, a number of named storms, passing within the 50 mile radius have significantly impacted the project area, including Dorian (2013), Ernesto (2006), Wilma (2005), Tammy (2005), Frances (2004), and Jeanne (2004). Damages from these storms, as well as from more distant storms causing indirect impacts, included substantial erosion and damage from winds, waves, and elevated water levels. 3.5 Storm Surge Storm surge is defined as the rise of the ocean surface above its astronomical tide level due to storm forces. Surges occur primarily as a result of atmospheric pressure gradients and surface stresses created by wind blowing over a water surface. Strong onshore winds pile up water near the shoreline, resulting in super-elevated water levels along the coastal region and inland waterways. In addition, the lower atmospheric pressure which accompanies storms also contributes to a rise in water surface elevation. Extremely high wind velocities coupled with low barometric pressures (such as those experienced in tropical storms, hurricanes, and very strong Northeasters) can produce very high, damaging water levels. In addition to wind speed, direction and duration, storm surge is also influenced by water depth, length of fetch (distance over water), and frictional characteristics of the nearshore sea bottom. An A-9

14 estimate of storm surge is required for the design of beach fill crest elevations. An increase in water depth may increase the potential for coastal flooding and allow larger storm waves to attack the shore. Figure A- 6. Historic storm tracks Hurricanes and Tropical Storms ( , 50 mile radius) The dune system at the northern end of the Jupiter-Carlin study area, just south of the south jetty, is relatively low and flat. This region has an elevation of around +11 ft-navd88 and is susceptible to overtopping from extreme storm surges. Further south, topographic surveys show that much of the dune reaches an elevation of +17 to +20 ft-navd88 which reduces the risk of overtopping due to extreme storm surges. This can be seen in The Florida Division of Emergency Management s Storm Tide Zone Map (Figure A- 7) for north Palm Beach County (FDEM, 2010). This map indicates that much of the north end of the project is susceptible to storm tides from hurricanes of category 1 through 3. South of Jupiter Beach Road, development and natural dune features have raised the elevation of the project area such that it is only susceptible to storm tides east of the dune line or along the inland portions of the barrier island. Storm surge levels versus frequency of occurrence were obtained from data compiled by the University of Florida for the Florida Department of Transportation (FDOT, 2003). Table A- 7 provides peak storm surge heights by return period for Jupiter-Carlin. The storm surge elevations presented include the effects of astronomical high tide and wave setup. A-10

15 Figure A- 7. Storm Surge Zones, North Palm Beach County, Florida (FDEM, 2010). Table A- 7. Storm Tide Elevations (FDOT Station 2504) Return Period (Years) Total Storm Tide Level (Feet, NAVD88) A-11

16 3.6 Sea Level Rise Relative Sea Level Rise Relative sea level (RSL) refers to local elevation of the sea with respect to land, including the lowering or rising of land through geologic processes such as subsidence and glacial rebound. It is anticipated that relative sea level will rise in the project area within the anticipated life of the project. To incorporate the direct and indirect physical effects of projected future sea level change on design, construction, operation, and maintenance of coastal projects, the U.S. Army Corps of Engineers (USACE) has provided guidance in the form of Engineering Regulation, ER (USACE, 2013). ER provides both a methodology and a procedure for determining a range of sea level change estimates based on global sea level change rates, the local historic sea level change rate, the construction (base) year of the project, and the design life of the project. Three estimates are required by the guidance, a Baseline (or Low ) estimate, which is based on historic sea level rise and represents the minimum expected sea level change, an Intermediate estimate (NRC Curve I), and a High estimate (NRC Curve III) representing the maximum expected sea level change. All three scenarios are based on the following eustatic sea level rise (sea level change due to glacial melting and thermal expansion of sea water) equation: EE(tt) = tt + bbtt 2 Where E(t) is the eustatic sea level rise (in meters); t represents years, starting in 1992 (the midpoint of the current National Tidal Datum Epoch of ), and b is a constant equal to 2.71E-5 (NRC Curve I), 7.00E-5 (NRC Curve II), and 1.13E-4 (NRC Curve III). This equation assumes a global mean sea level change rate of +1.7mm/year. In order to estimate the eustatic sea level change over the life of the project, the eustatic sea level rise equation is modified as follows: EE(tt 2 ) EE(tt 1 ) = (tt 2 tt 1 ) + bb(tt 2 2 tt 1 2 ) Where t 1 is the time between the project s construction date and 1992 and t 2 is the time between the end of the project life and In order to estimate the required Baseline, Intermediate, and High Relative Sea Level (RSL) changes over the life of the project, the eustatic sea level rise equation is further modified to include site specific sea level change as follows: RSL(t 2) RSL(t 1) = (e+m) (t 2 t 1) + b(t 2 2 t 12 ) Where RSL(t 1) and RSL(t 2) are the total RSL at times t 1 and t 2, and the quantity (e + M) is the local sea level rise in mm/year. Local sea level rise accounts for the eustatic change (1.7mm/year; ft/year) as well as uplift, subsidence, and other effects and is generally available from the nearest tide gage with a tidal record of at least 40 years. The constant b is equal to 0.0 (Baseline), 2.71E-5 (Intermediate), and 1.13E-4 (High). The Jupiter-Carlin project area is located approximately 80 miles from NOS gage # at Miami, Florida. The historical sea level rise rate taken from this gage was determined to be 2.39 mm/year ( ft/year) ( Given a project base year of 2018 and A-12

17 27 years remaining in the project life (project end date of 2045), a table of sea level change rates was produced for each of the three required scenarios. Figure A- 8 shows the sea level change rates, starting from the base year of 2018 and ending in 2045, the project end year. A graphic representation of the three levels of projected future sea level change for the life of the project is also provided. Average intermediate and high sea level rise rates were found to be ft/year and ft/year, respectively. The local rate of vertical land movement is approximated by subtracting regional MSL trend from local MSL trend. The regional mean sea level trend is assumed equal to the eustatic mean sea level trend of 1.7 mm/year. Therefore at Jupiter-Carlin, there is approximately 0.69 mm/year of movement (vertical shift of approximately mm/year). Figure A- 8. Relative Sea Level Change, Jupiter-Carlin ( Beach Responses to Sea Level Change This section evaluates how the sea level change scenarios outlined in the preceding section could affect future beach and shoreline behavior in the project area. The principal means by which sea level change would manifest itself on an open coast, sandy beach would be through changes to shoreline position and to beach volume. The following analyses are based on the assumption that sea level change would cause a change in the horizontal and vertical position of the beach profile. This phenomenon was first outlined by Per Bruun (1962). The theory states that an increase in water level causes the beach profile to shift upward and landward in response, in order to maintain an equilibrium shape. This shift causes both a shoreline change and a volumetric change as described in the following paragraphs. The application of Bruun s Rule in assessing coastal flood management measures is in accordance with A-13

18 USACE Engineering Technical Letter (ETL) (USACE, 2014) which provides guidance on procedures to evaluate sea level change. Additional information on incorporating sea level change into the evaluation of coastal flood management alternatives for St Lucie County is provided in Section 6.3.2: Applied Shoreline Change. Shoreline Change Per Bruun (1962) proposed a formula for estimating the rate of shoreline recession based on the local rate of sea level change. This methodology also includes consideration of the local topography and bathymetry. Bruun s approach assumes that with a change in sea level, the beach profile will attempt to reestablish the same bottom depths relative to the surface of the sea that existed prior to sea level change. That is, the natural profile will be translated upward and shoreward to maintain equilibrium. If the longshore littoral transport in and out of a given shoreline is equal, then the quantity of material required to re-establish the nearshore slope must be derived from erosion of the shore. Shoreline recession, X, resulting from sea level change can be estimated using Bruun s Rule, defined as: XX = SSWW (h + BB) Where S is the rate of sea level change; B is the berm height (approximately +7.5 feet NAVD88); h * is depth of closure (the depth beyond which there is no significant change over time in the shoreline profile; estimated to be approximately -15 feet NAVD88); and W * is the width of the active profile (approximately 900 feet). Figure A- 9. Shoreline Recession vs Year provides the resulting shoreline recession versus year for each of the three sea level rise scenarios. Note that shoreline recession is plotted relative to existing conditions at the project start year (i.e. all curves begin at 0.0 relative to 2018). The Bruun procedure is applicable to long straight sandy beaches with an uninterrupted supply of sand. Little is known about the rate at which profiles respond to changes in water level; therefore, this procedure should only be used for estimating long-term changes. The procedure is not a substitute for the analysis for historical shoreline and profile changes when determining historic (baseline) conditions. However, if little or no historical data is available, then historical analysis may be supplemented by this method to provide an estimate of the long-term erosion rates attributable to sea level rise. The offshore contours in the project area are not entirely straight and parallel; however, Bruun s Rule does provide an estimate of the potential shoreline changes within the project area attributable to a projected change in sea level. Volumetric Change Coastal Engineering Manual (CEM), Engineering Manual (USACE, 2002) gives guidance on how to calculate beach volume based on berm height, depth of closure, and translation of the shoreline (in this case, shoreline recession). Assuming that as an unarmored beach erodes, it maintains approximately the same profile above the seaward limit of significant transport the volume can be determined as: VV = (BB + h )XX A-14

19 Where B is the berm height, h * is the depth of closure, and X is the horizontal translation of the profile. Figure A- 10 provides the resulting volume lost versus year for each of the three sea level rise scenarios. Note that volume change is plotted relative to existing conditions at the project start year (i.e. all curves begin at 0.0 relative to 2018). 50 Shoreline Recession (Bruun's Rule) vs Year Jupiter Carlin, Palm Beach County Shoreline Recession (ft/yr) Year Baseline Intermediate High Figure A- 9. Shoreline Recession vs Year A-15

20 Estimated Volume Lost vs Year Jupiter Carlin, Palm Beach County Volume Lost (cy/ft/yr) Baseline Intermediate High Year Figure A- 10. Estimated Volume Lost Versus Year 4 Historical Shoreline Change Changes in mean high water (MHW) position provide a historical view of the behavior of the shoreline. Beach profiles are traditionally gathered by the FDEP, local sponsors, and USACE. Available beach surveys for Palm Beach County go back as far as However, the reliability of such historical profiles may be questionable. Additionally, some surveys were conducted over a span of years (i.e to 1973) without any indication of which portion of the shoreline was surveyed during which year. Knowing the year of the survey data is vital to the accuracy of the annual erosion rate. Therefore, based on a review of all available surveys, it was determined that profiles surveyed prior to 1972 would be included in the MHW analysis for informational purposes only. The Jupiter-Carlin segment of Palm Beach County is presently authorized as a Federal Hurricane Storm Damage Reduction (HSDR) project (now referred to as a Coastal Storm Risk Management or CSRM project). Initial construction of the project occurred in 1995, followed by periodic renourishments starting in In order to determine the historical (pre-project) erosion rate, surveys from 1995 to present were removed from the MHW analysis. MHW shoreline positions were measured at each DNR survey monument location, for each survey, along the proper azimuth (75 to 85 degrees dependent on monument measured clockwise from north). MHW change rates between 1883 and 1990 are tabulated in Table A- 9. A-16

21 Table A- 8. Mean High Water Shoreline Position Change In order to better interpret the shoreline change, the MHW position data was put into a graphical format (Figure A- 11). As seen in the figure, shoreline changes fluctuate over time along the study areas. Historically, the shoreline appears to be relatively stable. However, highly fluctuating periods of accretion and high erosion immediately south of the south jetty (R-13 to R-15) reflect that typical erosion down drift of the inlet is being compensated with nearly annual placement of maintenance material dredged from the inlet entrance channel and intracoastal waterway. Historical records available as far back as 1947 indicate placements of dredged material ranging from 40,000cy to over 200,000cy. Accretion over a majority of the project area (R-15 to R-19) between 1987 and 1990 also indicates at least one large scale placement event occurred during that time period. Given the unreliability of earlier profile data, uncertain survey dates, and essentially annual fill event(s) of varying volume and extent, it was determined that of the available data, the shoreline change rates from 1974 to 1987 give the best representation of the historical erosion rates for the project area. These erosion rates incorporate the reliability of annual dredged material placement as well as the uncertainty of the annual volume of each fill. 5 Effects of Adjacent Features 5.1 Jupiter Inlet Jupiter inlet lies in northern Palm Beach County, approximately 16 mi south of the St. Lucie Inlet and 11.7 mi north of the Lake Worth Inlet. Stabilized with jetties, the inlet supports navigation and maintains the outflow of the Loxahatchee River and the C-18 drainage canal. The Intracoastal Waterway (ICWW) crosses the Loxahatchee River immediately west of the inlet. Jupiter Inlet contributes to beach erosion by acting as a sediment sink. The stabilized inlet interrupts the net southerly longshore sediment transport that would otherwise nourish the project area. Tidal flood currents divert sediment from the coast into the inlet. Once inside the inlet, sediments tend to settle out into flood shoals. Tidal ebb currents also divert sediments along the coast farther seaward. These sediments also tend to settle out into ebb shoals as the tidal velocity decreases. The inlet s south jetty and the location of the ebb shoal return bar have historically dictated the limits of severe erosion. The ebb shoal, attaching to the shore between R-16 and R-19, has migrated over the years. While severe erosion generally occurs immediately south of inlets, slow long-term erosion may also occur further down-drift of the inlet due to the littoral drift deficit. A-17

22 Figure A- 11. MHW Changes, Jupiter-Carlin Study Area A-18

23 Three governmental entities routinely dredge in the vicinity of Jupiter Inlet. Palm Beach County acts as the local sponsor for the existing Jupiter-Carlin segment of the Palm Beach County SPP. The Florida Inland Navigation District (FIND) acts as the local sponsor for ICWW maintenance which disposes of material near Jupiter Inlet along the project shoreline (typically just south of the jetty in the vicinity of R- 13 to R-17). And the Jupiter Inlet District (JID) acts as the local sponsor for Jupiter Inlet and is responsible for periodically dredging a sand trap located in the inlet throat. Table A- 10 presents a history of dredging in the inlet (sand trap and ebb shoal) and ICWW since Note that prior to 1970 all material from the ICWW was placed upland. After 1970 material was placed on the shoreline south of the inlet. 6 Beach-fx Life-Cycle Shore Protection Project Evolution Model Federal participation in Hurricane and Storm Damage Reduction (HSDR) projects is based on a favorable economic justification in which the benefits of the project outweigh the costs. Determining the Benefit to Cost Ratio (BCR) requires both engineering (project performance and evolution) and planning (alternative analysis and economic justification) analyses. The interdependence of these functions has led to the development of the life-cycle simulation model Beach-fx. Beach-fx combines the evaluation of physical performance and economic benefits and costs of shore protection projects (Gravens et. al., 2007), particularly beach nourishment, to form the basis for determining the justification for Federal participation. This section describes the engineering aspects of the Beach-fx model. 6.1 Background & Theory Beach-fx is an event-driven life-cycle model. USACE guidance (USACE, 2006) requires that flood damage reduction studies include risk and uncertainty. The Beach-fx model satisfies this requirement by fully incorporating risk and uncertainty throughout the modeling process (input, methodologies, and output). Over the project life-cycle, typically 50 years, the model estimates shoreline response to a series of historically based storm events. These plausible storms, the driving events, are randomly generated using a Monte Carlo simulation. The corresponding shoreline evolution includes not only erosion due to the storms, but also allows for storm recovery, post-storm emergency dune and/or shore construction, and planned nourishment events throughout the life of the project. Risk based damages to structures are estimated based on the shoreline response in combination with pre-determined storm damage functions for all structure types within the project area. Uncertainty is incorporated not only within the input data (storm occurrence and intensity, structural parameters, structure and contents valuations, and damage functions), but also in the applied methodologies (probabilistic seasonal storm generation and multiple iteration, life cycle analysis). Results from multiple iterations of the life cycle can be averaged or presented as a range of possible values. The project site itself is represented by divisions of the shoreline referred to as Reaches. Because this term may also be used to describe segments of the shoreline to which project alternatives are applied, Beach-fx reaches will be referred to in this appendix as Model reaches. Model reaches are contiguous, morphologically homogenous areas that contain groupings of structures (residences, businesses, walkovers, roads, etc ), all of which are represented by Damage Elements (DEs). DEs are grouped within divisions referred to as Lots. Figure A- 12 shows a graphic depiction of the model setup. For further details about the specifics of Lot extents and DE grouping see the Economics Appendix. A-19

24 Table A- 9. Dredging History (Average Annual) in the Vicinity of Jupiter Inlet A-20

25 Figure A- 12. Beach-fx Model Setup Representation Each model reach is associated with a representative beach profile that describes the cross-shore profile and beach composition of the reach. Multiple model reaches may share the same representative beach profile while groupings of model reaches may represent a single design reach. For Jupiter-Carlin, the project area consists of a single design reach originally divided into eight model reaches. Table A- 11 provides model reach identifiers as well as corresponding FDEP R-monument locations. A review of the specific project limits (R-13 to R-19) caused the northern most model reach (JC 13-1) to be dropped from the analysis. Figure A- 13 shows each of the final model reach locations graphically. Table A- 10. Model Reaches Model Reaches R-monuments JC 13 Jetty to R-13 JC 14 R-13, R-14 JC 15 R-15 JC 16 R-16 JC 17 R-17 JC 18 R-18 JC 19 R-19 A-21

26 Figure A- 13. Model Reaches Relative to FDEP R-monuments Implementation of the Beach-fx model relies on a combination of meteorology, coastal engineering, and economic analyses and is comprised of four basic elements: Meteorological driving forces Coastal morphology Economic evaluation Management measures The subsequent discussion in this section addresses the basic aspects of implementing the Beach-fx model. For a more detailed description of theory, assumptions, data input/output, and model implementation, refer to Gravens et al. (2007), Males et al. (2007), and USACE (2009). 6.2 Meteorological Driving Forces The predominant driving force for coastal morphology and associated damages within the Beach-fx model is the historically based set of storms that is applied to the life-cycle simulation. Because the eastern coast of Florida is subject to seasonal storms, tropical storms (hurricanes) in the summer months and extra-tropical storms (Northeasters) in the winter and fall months, the plausible storms A-22

27 dataset for Palm Beach County is made up of both types. Derived from the historical record of the region, the plausible storm set is based on 30 tropical storms occurring between 1887 and 2004 and 56 extra-tropical storms, occurring between 1994 and Because tropical storm events tend to be of limited duration, passing over a given site within a single portion of the tide cycle, it is assumed that any of the historical storms could have occurred during any combination of tidal phase and tidal range. Therefore, each of the 30 tropical storms surge hydrographs was combined with possible variations in the astronomical tide. This was achieved by combining the peak of each storm surge hydrograph with the astronomical tide at high tide, mean tide falling, low tide, and mean tide rising for each of three tidal ranges corresponding to the lower quartile, mean, and upper quartile tidal ranges. This resulted in 12 distinct combinations for each historically based tropical storm and a total of 360 tropical storm conditions in the plausible storm dataset. Due to their generally extended durations, extra-tropical storms in the historical record tend to occur over complete tide cycles. Therefore, it can be assumed that the storm hydrograph of each of the 56 historical extra-tropical storms is sufficient without combining with possible variations of the astronomical tide. The entire plausible storm suite therefore consists of a total of 416 tropical and extra-tropical storms. In addition to the plausible storm dataset, the seasonality of the storms must also be specified. The desired storm seasons are based on the assumption that each plausible storm takes place within the season in which the original historical storm occurred. The probability of both tropical and extratropical storms is defined for each season through the Probability Parameter. The Probability Parameter is determined for each season and storm type by dividing the number of storms within the season by the total number of years in the storm record (extra-tropical or tropical). Four storm seasons were specified for Palm Beach County (Table A- 12). Table A- 11. Palm Beach County Beach-fx Storm Seasons Storm Season Start Date End Date Probability Parameter Extra-Tropical Storm Probability Parameter Tropical Storm Extratrop Winter/Spring Dec 1 Apr Tropical Early Summer May 1 Jul Tropical Peak Aug 1 Sep Extratrop/Tropical Oct 1 Nov The combination of the plausible storm dataset and the specified storm season allows the Beach-fx model to randomly select storms that fall within the season currently being processed. For each storm selected, a random time within the season is chosen and assigned as the storm date. The timing of the entire sequence of storms is governed by a pre-specified minimum storm arrival time. A minimum arrival time of 7 days (the recommended interval absent atypical site specific historical storm behavior) was specified for Palm Beach County. Based on this interval the model attempts to place subsequent storm events outside of a 14 day window surrounding the date of the previous storm (i.e. a minimum of 7 days prior to the storm event and a minimum of 7 days following the storm event). Due to the probabilistic nature of Beach-fx, the minimum arrival time may be overridden by the model during the course of the life cycle analysis. A-23

28 6.3 Coastal Morphology The Beach-fx model estimates changes in coastal morphology through four primary mechanisms: Shoreline storm response Applied shoreline change Project-induced shoreline change Post-storm berm recovery Combined, these mechanisms allow for the prediction of shoreline morphology for both with and without project conditions Shoreline Storm Response Shoreline storm response is determined by applying the plausible storm set that drives the Beach-fx model to simplified beach profiles that represent the shoreline features of the project site. For this study, application of the storm set to the idealized profiles was accomplished with the SBEACH coastal processes response model (Larson and Kraus, 1989). SBEACH is a numerical model which simulates storm-induced beach change based on storm conditions, initial profiles, and shoreline characteristics such as beach slope and grain size. Output consists of post-storm beach profiles, maximum wave height and wave period information, and total water elevation including wave setup. Pre- and post-storm profiles, wave data, and water levels can be extracted from SBEACH and imported into the Beach-fx Shore Response Database (SRD). The SRD is a relational database populated with the SBEACH simulation results of all plausible storms impacting a pre-defined range of anticipated beach profile configurations Representative Profiles In order to develop the idealized SBEACH profiles from which the SRD was derived, it was necessary to first develop representative profiles for the project shoreline. The number of representative profiles developed for any given project depends on the natural variability of shoreline itself. Typically, historical profiles at each FDEP R-monument would be compared over time, aligned, and then averaged into a composite profile representative of the shoreline shape at that given R-monument location. Composite profiles would then be compared and separated into groupings according to the similarity between the following seven dimensions: Upland elevation Dune slope Dune height Dune width Berm height Berm width Foreshore slope A-24

29 However, in a Section 934 study the future without project shoreline and the future with project shoreline represent two unrelated sets of physical characteristics. The future without project shoreline is the projected shoreline at the project base year assuming that no Federal project was ever constructed. The future with project shoreline is the projected shoreline at the project base year assuming that the Federal project was constructed and maintained as authorized. Therefore, the future without project and future with project profiles for a Section 934 study would be represented by two separate sets of representative profiles. Initially the two (required) sets of representative profiles were developed for the Jupiter Carlin Study. The profile dimensions were similar, but the curvature of the shoreline and distance from the R- monuments along the project were significantly different. This presented a problem when applying the Beach-fx model. The Beach-fx model was developed to compare the storm response of a future without project (existing) shoreline with a proposed project shoreline that is built onto that same future without project shoreline. However, when the model was used to compare the Gasparilla future without project condition (projected as if no project had been built) with the future with project condition (using a shoreline that was influenced by the existing project) the results could not be compared in a logical fashion. One to one comparison of with and without project profiles showed a number of locations where damages increased for the with-project condition. A deeper look into model output files showed that the difference between the starting shorelines (relative to the project baseline or ECL) made a meaningful comparison impossible. Therefore, a single shoreline was developed to represent both the with and without project conditions Future Without Project (FWOP) and Future With Project (FWP) Profiles For both the FWOP and FWP scenarios, the project start year and base year are 2018 and 2019, respectively. Therefore, the project shoreline must reflect expected 2018 shoreline dimensions. In 2015 the project was restored to 2012 pre-hurricane Sandy dimensions as part of a Federal Flood Control and Coastal Emergency (FCCE) nourishment effort. Therefore, because 2015 surveys were unavailable at the time that the model inputs were developed, the 2015 restored shoreline was estimated to be the same as the 2012 measured shoreline. By applying three years of background erosion to this restored 2015 (2012 measured) shoreline, 2018 shoreline dimensions were approximated. Table A- 14 provides dimensions for each of the idealized representative FWP Beach-fx profiles. Table A- 12. Dimensions of Idealized FWP Pre-Storm Representative Profiles (2018 Shoreline) Profile R-monuments Represented Dune Width Dune Slope Berm Width Upland Elevation (ft-navd88) Dune Height (ft-navd88) Berm Elevation (ft-navd88) Foreshore Slope (V:H,ft) (ft) (V:H, ft) (ft) JC13 R : :7.1 JC14 R : :10 JC15 R : :10 JC16 R : :10 JC17 R : :10 JC18 R : :10 JC19 R : :8.3 A-25

30 In accordance with Section 934 guidance, the FWP analysis consists primarily of determining if the authorized design template is still economically justified. According to the original authorization, the design template is defined as the 1990 MHW line. Figure A- 21 to Figure A- 27 show the projected 2018 shoreline, the idealized FWP profiles (as defined in Table A- 14), and the location of the 1990 MHW. Note that for Beach-fx, the FWOP and FWP must share the same upland elevation, berm elevation, and dune and foreshore slopes SBEACH Methodology SBEACH simulates beach profile changes that result from varying storm waves and water levels. These beach profile changes include the formation and movement of major morphological features such as longshore bars, troughs, and berms. SBEACH is a two-dimensional model that considers only crossshore sediment transport. The model assumes that simulated profile changes are produced only by cross-shore processes. Longshore wave, current, and sediment transport processes are not included. SBEACH is an empirically based numerical model, which was formulated using both field data and the results of large-scale physical model tests. Input data required by SBEACH describes the storm being simulated and the beach of interest. Basic requirements include time histories of wave height, wave period, water elevation, beach profile surveys, and median sediment grain size. Figure A- 14. Projected 2018 and Eroded Idealized Profile: Model Reach JC 13 A-26

31 Figure A- 15. Projected 2018 and Eroded Idealized Profile: Model Reach JC 14 Figure A- 16. Projected 2018 and Eroded Idealized Profile: Model Reach JC 15 A-27

32 Figure A- 17. Projected 2018 and Eroded Idealized Profile: Model Reach JC 16 Figure A- 18. Projected 2018 and Eroded Idealized Profile: Model Reach JC 17 A-28

33 Figure A- 19. Projected 2018 and Eroded Idealized Profile: Model Reach JC 18 Figure A- 20. Projected 2018 and Eroded Idealized Profile: Model Reach JC 19 A-29

34 SBEACH simulations are based on six basic assumptions: Waves and water levels are the major causes of sand transport and profile change Cross-shore sand transport takes place primarily in the surf zone The amount of material eroded must equal the amount deposited (conservation of mass) Relatively uniform sediment grain size throughout the profile, The shoreline is straight and longshore effects are negligible Linear wave theory is applicable everywhere along the profile without shallow-water wave approximations Once applied, SBEACH allows for variable cross shore grid spacing, wave refraction, randomization of input waves conditions, and water level setup due to wind. Output data consists of a final calculated profile at the end of the simulation, maximum wave heights, maximum total water elevations plus setup, maximum water depth, volume change, and a record of various coastal processes that may occur at any time-step during the simulation (accretion, erosion, over-wash, boundary-limited run-up, and/or inundation) SBEACH Calibration Calibration of the SBEACH model was performed using wave height, wave period, and water level information from a combined time series of Hurricanes Frances and Jeanne (2004) (Figure A- 28). Calibration of the model is necessary to ensure that the SBEACH model is tuned to provide realistic shore responses that are representative of the specific project location. Figure A- 21. Hurricane Frances and Jeanne Wave and Water Level Data for SBEACH Calibration A-30

35 Pre-storm (August 2004) and post-storm (November 2004) shoreline profiles were obtained from FDEP. Using the pre-storm profiles, SBEACH was then run with a range of values for an array of calibration parameters. Table A- 15 provides the relevant beach characteristic and sediment transport calibration parameters as well as their final calibrated values. Calibration parameters were verified using wave height, wave period, and water level information from Hurricanes Floyd and Irene (1999) (Figure A- 29). Table A- 13. SBEACH Calibrated Beach Characteristic and Sediment Transport Parameters Beach Characteristic Sediment Transport Parameter Calibrated Value Parameter Calibrated Value Landward Surf Zone Depth 1.0 m Transport Rate Coefficient 2.5e-06 (m4/n) Overwash Transport Parameter 0.0 Effective Grain Size 0.35 mm Coefficient for Slope- Dependent Term Transport Rate Decay Maximum Slope Prior to Coefficient Multiplier Avalanching Water Temperature 25degC Figure A- 30 to Figure A- 43 show calibration and verification results for each of the project profiles. Beach-fx extracts information from SBEACH results only from the sub-aerial portion of the profile. The mean low water line (MLW) is indicated on each figure. Beach-fx extracts dimensional changes to the dune height, dune width, and berm width. Good agreement between measured and modeled dimensional changes were obtained in the sub-aerial regions. Note that some measured profiles were limited in extent, impacting SBEACH results. This is most notable with pre-floyd/irene profiles taken at R-14 and R-15. Figure A- 22. Hurricane Floyd and Irene Wave and Water Level Data for SBEACH Verification A-31

36 SBEACH Simulations Calibrated Jupiter-Carlin SBEACH simulations were run for each of the existing, future without project and with project idealized profiles in combination with each of the tropical and extra-tropical storms in the plausible storm database. From these profiles, changes in the key profile dimensions were extracted and stored in the Jupiter-Carlin Beach-fx SRD Applied Shoreline Change The applied shoreline change rate (in feet per year) is a Beach-fx morphology parameter specified at each of the model reaches. It is a calibrated parameter that, combined with the storm-induced change generated internally by the Beach-fx model, returns the historical shoreline change rate for that location. The target shoreline change rate is an erosion or accretion rate derived from the MHW rate of change determined at each R-monument location (see Section 4 Historical Shoreline Change). Figure A- 44 shows the target shoreline change rates. During Beach-fx calibration, applied erosion rates were adjusted for each model reach and the Beach-fx model was run for hundreds of iterations over the 50-year project life cycle. Calibration is achieved when the rate of shoreline change, averaged over hundreds of life cycle simulations, is equal to the target shoreline change rate Profile R-13 Frances & Jeanne (2004) Elevation (ft-navd88) Aug-04 Nov-04 SBEACH MLW Distance from R-monument (ft) Figure A- 23. SBEACH Calibration: Profile R-13 A-32

37 Profile R-13 Floyd & Irene (1999) Elevation (ft-navd88) Jun-99 Nov-99 SBEACH MLW Distance from R-Monument (ft) Figure A- 24. SBEACH Verification: Profile R Profile R-14 Frances & Jeanne (2004) 15 Elevation (ft-navd88) Aug-04 Nov-04 SBEACH MLW Distance from R-monument (ft) Figure A- 25. SBEACH Calibration: Profile R-14 A-33

38 Profile R-14 Floyd & Irene (1999) Elevation (ft-navd88) Jun-99 Nov-99 SBEACH MLW Distance from R-Monument (ft) Figure A- 26. SBEACH Verification: Profile R Profile R-15 Frances & Jeanne (2004) 15 Elevation (ft-navd88) Aug-04 Nov-04 SBEACH MLW Distance from R-monument (ft) Figure A- 27. SBEACH Calibration: Profile R-15 A-34

39 Profile R-15 Floyd & Irene (1999) Elevation (ft-navd88) Jun-99 Nov-99 SBEACH MLW Distance from R-Monument (ft) Figure A- 28. SBEACH Verification: Profile R Profile R-16 Frances & Jeanne (2004) 15 Elevation (ft-navd88) Aug-04 Nov-04 SBEACH MLW Distance from R-monument (ft) Figure A- 29. SBEACH Calibration: Profile R-16 A-35

40 Profile R-16 Floyd & Irene (1999) Elevation (ft-navd88) Jun-99 Nov-99 SBEACH MLW Distance from R-Monument (ft) Figure A- 30. SBEACH Verification: Profile R Profile R-17 Frances & Jeanne (2004) 15 Elevation (ft-navd88) Aug-04 Nov-04 SBEACH MLW Distance from R-monument (ft) Figure A- 31. SBEACH Calibration: Profile R-17 A-36

41 Profile R-17 Floyd & Irene (1999) Elevation (ft-navd88) Jun-99 Nov-99 SBEACH MLW Distance from R-Monument (ft) Figure A- 32. SBEACH Verification: Profile R Profile R-18 Frances & Jeanne (2004) 15 Elevation (ft-navd88) Aug-04 Nov-04 SBEACH MLW Distance from R-monument (ft) Figure A- 33. SBEACH Calibration: Profile R-18 A-37

42 Profile R-18 Floyd & Irene (1999) Elevation (ft-navd88) Jun-99 Nov-99 SBEACH MLW Distance from R-Monument (ft) Figure A- 34. SBEACH Verification: Profile R Profile R-19 Frances & Jeanne (2004) Elevation (ft-navd88) Aug-04 Nov-04 SBEACH MLW Distance from R-monument (ft) Figure A- 35. SBEACH Calibration: Profile R-19 A-38

43 Profile R-19 Floyd & Irene (1999) Elevation (ft-navd88) Jun-99 Nov-99 SBEACH MLW Distance from R-Monument (ft) Figure A- 36. SBEACH Verification: Profile R-19 It is through the applied erosion rates that sea level change is incorporated into the Beach-fx shoreline change simulations. The calibrated applied erosion rates, based on historical shoreline change and the existing measured sea level rate of change, represents the baseline (low) sea level change condition. By adding the change in shoreline recession predicted by Bruun s Rule (See Section 3.6.2: Beach Responses to Sea Level Change) for the intermediate and high sea level change scenarios to the calibrated applied erosion rates at each Model Reach, adjusted applied erosion rates can be determined. Figure A- 45 shows target erosion rates, corresponding calibrated applied erosion rates (baseline sea level change), and resulting adjusted applied erosion rates (intermediate and high) sea level change Project Induced Shoreline Change The project induced shoreline change rate accounts for the alongshore dispersion of placed beach nourishment material. Beach-fx requires the use of shoreline change rates in order to represent the planform diffusion of the beach fill alternatives after placement. Traditionally the one-dimensional shoreline change model GENESIS (Hanson and Kraus, 1989), a PC-based program capable of simulating long term spatial changes in longshore transport, has been employed for USACE feasibility studies. However, model setup, calibration, verification, and application to an array of beach renourishment alternatives can be complex and time consuming. Although the introduction of the GenCade model, an updated variation of GENESIS, has helped streamline model setup, the complete application process is still a significant effort. A-39

44 Figure A- 37. Target MHW Shoreline Change Rate Figure A- 38. Target MHW Shoreline Change and Applied Erosion Rates A-40

45 In order to bring the analysis more in line with the accelerated schedules required under SMART Planning guidelines, an alternative methodology was employed. Engineering Manual EM Design of Beach Fills (USACE, 1995) provides guidance on the selection of shoreline change models. Four acceptable alternatives are discussed: o o o o GENESIS One-dimensional model (PC based) Dean and Yoo (1992) One line analytical model (spreadsheet/calculator based) Multi-contour 3D Three dimensional model with variable profile and longshore capabilities (PC based) Fully 3D Model Three dimensional model that calculate waves and currents in addition to sediment transport (PC based) Of the alternatives, the one line analytical model is simplest to apply and produces valid planform diffusion estimates for variable fill widths and lengths. It should be noted that the governing equation within the GENESIS and GenCade models is a one line analytical solution One Line Analytical Model While Dean and Yoo provides the basic governing formulations for assessing shoreline change rates, it does not specify a discrete analytical solution. These governing formulations, based on the conservation of sand combined with sediment transport, have existed for several decades. In that time, many analytical solutions have been developed to solve them. Because the analytical solution presented by Larson et al. (1987) is the closest in formulation to the GENESIS model traditionally used in more complex USACE applications, it was selected as the one-line model for use with the Jupiter Carlin project Governing Equations As presented by Dean and Yoo, shoreline response can be derived from the following governing equations: (1) Conservation of Sand (one dimensional form) Where + 1 (h + BB) = 0 y = cross-shore distance t = time h * = depth of closure B = berm elevation Q = long shore sediment transport x = long-shore distance (2) Sediment Transport (one dimensional form) II = KKPP llll A-41

46 Where I = immersed weight sediment transport rate (a function of Q) K = non-dimensional sediment transport proportionality factory P ls = long shore energy flux factor (a function of the breaking wave climate) One Line Analytical Solution Based on the governing formulations, a number of analytical solutions are possible. The solution derived by Larson et al. was selected based on compatibilities to the derivation of the one line model on which GENESIS and GenCade are formulated Larson et al. The analytical solution for shoreline evolution derived by Larson et al. can be described by: Where yy(xx, tt) = 1 2 yy aa xx + xx oo eeeeee + eeeeee aa 2 εεεε 2 εεεε a = one half of the length of the fill y o = original cross-shore width of the fill x = long-shore distance (where x = 0 is the center point of the fill) t = time (where t = 0 is initial placement) ε = diffusion coefficient The diffusion coefficient is defined as: εε = 2QQ (h + BB) Where Q can be computed using the CERC equation, given as: Where QQ = 5 KKHH 2 bb gg sin (2θθ) λλ 16(ss 1)(1 pp) K = non-dimensional sediment transport proportionality factory (see Section ) H b = breaker height (see Section ) g = acceleration due to gravity λ = breaking wave height proportionality factor θ = angle of wave approach s = specific gravity of sediment p = porosity of sediment A-42

47 Input Parameters Breaker Wave Height The breaker wave height is an estimate of the height of waves as they arrive and break on a given beach. As wave trains are composed of irregular waves with heights and periods that are variable in both time and space, it is necessary to develop a single breaker height H b that represents the wave energy present at the shoreline due to the wave climate of the project area. Methodologies for estimating H b have been developed, generally from laboratory or observed data, since the 1940 s. There are many formulations available. One of the most commonly accepted methods of estimating H b is based on deep-water wave characteristics (USACE, 1984). It is expressed as: Where H o = unrefracted deep-water wave height L o = deep-water wave period HH bb HH = 1 oo 3.3( HH oo LL ) 1 3 oo For the Jupiter Carlin project, the representative deep-water wave height for the estimate was determined using hindcast wave data from WIS station # Higher energy deep-water waves disperse a great deal of energy through whitecapping, wave interactions, and breaking in waters well seaward of the nearshore breaking zone. Therefore, reducing the full deep-water dataset to an approximation of those waves that reach and deliver energy to the nearshore breaker zone will give a more accurate representation of the energy that is moving the sediment on a daily basis. It is this daily dispersion that is the most relevant as input into the Beach-fx model. Erosion due to storms is already accounted for through the separately developed (SBEACH based) storm response database. A percent occurrence breakdown of deep-water waves by height and period indicates that the majority of waves have deep-water wave heights of less than 2meters (6.6 feet) and periods of less than 6 seconds. To capture the energy of these lower energy waves, the average wave height of all waves falling between 0 and 2 meters (6.6 feet) in height with periods of less than 6 seconds was taken. Using the high end of the wave period range (6 seconds), the deep-water wavelength was determined to be feet. Combined with a the average wave height of the 0 to 2m (6.6 feet) range (found to be 0.63 meters or 2.1 feet), the representative value of H b was estimated to be 2.8 feet Wave Angle Although, the full energy of the deep-water wave climate was reduced in order to develop the representative nearshore breaker height, the representative direction of wave approach, θ, was taken to be the average dominant wave direction of the all of the waves in the deep-water dataset. This allowed the net overall incident wave energy direction (and the net sediment transport direction of the project area) to be preserved. This was accomplished by taking the average WIS wave direction for all waves regardless of wave height or periods. The average deep-water wave direction was found to be 48 o, measured clockwise from 0 o due north. This translated into a local shore normal wave direction of A-43

48 32 o (Figure A- 46). The deep water wave direction was then transformed using Snell s Law into a nearshore representative wave direction. Snell s Law is given as: Where SSSSSS(θθ nn ) = CC nn CC oo SSSSSS(θθ oo ) θo = representative deep-water wave direction (32 o relative to shore normal) C o = deep water wave celerity defined by: CC oo = gggg 2ππ Where g = 32.2 ft/sec 2 and T= average wave period of the full WIS dataset (8 seconds) C n = nearshore wave celerity defined by CC nn = ggh Where h = nearshore depth (taken to be depth of closure) Applying Snell s Law for the described parameters, the direction of wave approach was determined to be 19 o counter-clockwise relative to shore normal. Deepwater and nearshore wave angles relative to the shoreline are shown in Figure A Non-dimensional Sediment Transport Coefficient, K The sediment transport coefficient K can be highly variable. It is dependent on sediment characteristics, properties of the suspension medium, and local wave climate. Small changes in any of the environmental or sediment factors can have a significant impact on the value of K. This can be problematic as many of these factors vary in both time and space. Most recommended values of K in literature and guidance are based on field measurements and can vary widely. USACE 1984 recommends a value of 0.39 based on the original field study by Komar and Inman (1970). Bodge and Kraus (1991) used the same study to derive a recommendation of Schoonees and Theron (1993, 1994) used compiled field measurements from multiple sources to derive an approximation of 0.2. Numerous analytical formulas also exist for estimating K. A simplified estimate based on grain size presented by USACE (2002) was originally formulated by Komar (1988) as: KK = 1.4ee 2.5DD 50 Where D 50 is grain size. For the Jupiter Carlin project where grain size was determined to be 0.35mm, this results in an estimated value of K = Given its variability, K, can be set initially based on known or generally accepted parameter values, and then fine-tuned using measured or historical data for the project site. GENESIS applications are calibrated in just this manner, where K is adjusted to maximize replication of observed shoreline A-44

49 changes and longshore sediment transport rates. A similar principle can be used in application of the one-line model. Figure A- 39. Deep water and Nearshore Wave Angles Calibration In order to apply a one-line model to Jupiter Carlin, it is necessary to calibrate the model using available data. In the case of Jupiter Carlin, best available data are measured post-fill erosion rates collected from annual monitoring reports. This data from the previous fill event can be used to calibrate the model by determining the optimum value of K. The model can then be applied to renourishment templates of different dimension. Table A- 16 provides dimensions for the existing Jupiter Carlin project. Table A- 17 provides the average post-project recession rates as measured between 2003 and 2010 (the seven year renourishment interval) following the most recent placement event for which comprehensive data is available. Measurements were taken at seven FDEP R-monuments, R-13 to R-19. The very low erosion losses at the north end of the project at R-13 are due to the regular placement of dredged fill (by local authorities) from the inlet at this hotspot location. This may also be the reason for the relatively low end losses shown at R-19 at the south end. Though local placement information for this specific location was not available, annual monitoring indicates sudden accretion following periods of heavy erosion. Local placement at a hotspot combined with sediment moving south from the north portion of the project is assumed. Because the end losses are not likely to be predicted well by any model at R-13 and R-19, the focus of the calibration was at the more central portion of the fill between R-14 and R-18. Table A- 14. Existing Jupiter Carlin Project Dimensions Initial Fill Width Y o 110 feet Fill Length l 5,600 feet Depth of Closure h 15 ft-navd88 Berm Elevation B 7.5 ft-navd88 A-45

50 Optimizing K Using initial estimates for K as detailed previously, a range of values from 0.2 to 0.6 were used with the Larson et al. one-line model over a period of seven years. Average recession rates were determined at each of the seven R-monument locations. The absolute difference between measured and predicted recession was then taken. Figure A- 47 shows the difference between measured and predicted values for the wide range of K values employed. Difference values averaged over R-14 to R-18 are shown in Figure A- 48. Based on these values it is apparent that the optimum value of K falls roughly between 0.4 and 0.5. Further refinement of the assumed range of K (Figure A- 49 to Figure A- 50) results in a final optimized value for K of Table A- 15. Measured Average Annual Shoreline Change R-monument Average Annual Shoreline Change (feet) R R R R R R R Absolute Difference between Measured and Predicted Annual Shoreline Change, Larson et. al (K = 0.2 to 0.6) Absolute Difference (feet) R-14 R-15 R-16 R-17 R-18 R-monument Figure A- 40. Absolute Difference between Measured and Predicted Annual Shoreline Change (K=0.2 to 0.6), Larson et al. A-46

51 Average Absolute Difference between Measured and Predicted Annual Shoreline Change (K = 0.4 to 0.8) Average Absolute Difference (feet) K Larson et. al Figure A- 41. Average Absolute Difference between Measured and Predicted Annual Shoreline Change (K=0.2 to 0.6) 9 Absolute Difference between Measured and Predicted Annual Shoreline Change, Larson et. al (K = 0.40 to 0.46) Absolute Difference (feet) R-14 R-15 R-16 R-17 R-18 R-monument Figure A- 42. Absolute Difference between Measured and Predicted Annual Shoreline Change (K=0.40 to 0.46), Larson et al. A-47

52 Average Absolute Difference between Measured and Predicted Annual Shoreline Change (K = 0.4 to 0.46) Average Absolute Difference (feet) K Larson et. al Figure A- 43. Average Absolute Difference between Measured and Predicted Annual Shoreline Change (K=0.40 to 0.46) Shoreline Change Rates Table A- 18 provides the final parameters for determining shoreline change rates for Jupiter Carlin. Due to nearly annual local placement events of variable size and location, calibration of the one line model(s) was based on the optimization of K through comparison of measured and predicted annual shoreline change rates averaged over the full renourishment cycle. This captures the overall trend of the nourished shoreline and indirectly accounts, to the extent possible, for the influence of local fill events. Table A- 16. Final Parameters for Determining Shoreline Change Shoreline Change Key Input Parameters Breaker height H b 2.8 feet Angle of wave approach (degrees shore normal) θ 19 o Optimized sediment transport proportionality factory K 0.42 Breaking wave height proportionality factor λ 0.78 Specific gravity of sediment (quartz sand) s 2.65 Porosity of sediment (quartz sand) p 0.4 Figure A- 51 shows the annual shoreline change rates from Larson et al. Because the Larson et al. model is the closest in formulation to the GENESIS model traditionally used in more complex applications, it is considered to be an appropriate one-line model for use with the Jupiter Carlin project. A-48

53 Average Annual Shoreline Change Rate Average Annual Shoreline Change (feet) Larson et. al R-13 R-14 R-15 R-16 R-17 R-18 R-19 R-monument Figure A- 44. Average Annual Shoreline Change Rate from Larson et al Performance The project induced shoreline change rates calculated using the one-line model do not take into account the improved performance of beach nourishment projects that comes with project maturation. That is, theory and beach nourishment experience has shown that dispersion losses at a beach nourishment project tend to decrease with the number of project nourishments. Neither does Beach-fx factor in this phenomena. In order to prevent underestimating project performance and benefits, early Beach-fx users from within the coastal engineering community of practice determined that based on the behavior of previous storm damage reduction projects along the east coast of Florida, it can be assumed for the sake of this study that there will be a 20% reduction in shoreline change rates following each consecutive renourishment cycle Post Storm Berm Recovery Post storm recovery of eroded berm width after passage of a major storm is a recognized process. Although present coastal engineering practice has not yet developed a predictive method for estimating this process, it is an important element of post-storm beach morphology. Within Beach-fx, post-storm recovery of the berm is represented in a procedure in which the user specifies the percentage of the estimated berm width loss during the storm that will be recovered over a given recovery interval. It is important to note that the percentage itself is not a stand alone parameter that is simply applied during the post storm morphology computations. The percentage of berm recovery is estimated prior A-49

54 to model calibration and becomes a tunable calibration parameter to ensure model convergence (when the model reproduces the target erosion rates as discussed in Section Applied Shoreline Change). Based on recommendations by the model developer regarding east coast Florida shorelines, review of available historical FDEP profiles that would qualify as pre- and post- storm, and successful model calibration a recovery percentage of 90% over a recovery interval of 21 days was determined to be appropriate for Palm Beach County. 6.4 Economic Evaluation The Beach-fx model analyzes the economics of shore protection projects based on the probabilistic nature of storm associated damages to structures in the project area. Damages are treated as a function of structure location and construction, the intensity and timing of the storms, and the degree of protection that is provided by the natural or constructed beach. Within the model, damages are attributed to three mechanisms: Erosion (through structural failure or undermining of the foundation) Flooding (through structure inundation levels) Waves (though the force of impact) Although wind may also cause shoreline damage, shore protection projects are not designed to mitigate for impacts due to wind. Therefore, the Beach-fx model does not include this mechanism. Damages are calculated for each model reach, lot, and damage element following each storm that occurs during the model run. Erosion, water level, and maximum wave height profiles are determined for each individual storm from the lookup values in the previously stored SRD. These values are then used to calculate the damage driving parameters (erosion depth, inundation level, and wave height) for each damage element. The relationship between the value of the damage driving parameter and the percent damage incurred from it is defined in a user-specified damage function. Two damage functions are specified for each damage element, one to address the structure and the other to address its contents. Damages due to erosion, inundation, and wave attack are determined from the damage functions and then used to calculate a combined damage impact that reduces the value of the damage element. The total of all FWOP damages is the economic loss that can be mitigated by the shore protection project. A thorough discussion of the economic methodology and processes of Beach-fx can be found in the Economics Appendix. 6.5 Management Measures Shoreline management measures that are provided for in the Beach-fx model are emergency nourishment and planned nourishment. A-50

55 6.5.1 Emergency Nourishment Emergency nourishments are generally limited beach fill projects conducted by local governments in response to storm damage. The Jupiter-Carlin Segment of Palm Beach County does not have a consistent history of emergency nourishment in response to storm related erosion. The project site instead is protected by semi-regular placement of maintenance material taken from the ICWW and Jupiter Inlet (see Section 5: Effects of Adjacent Features). Therefore, this management measure was not included in the St Lucie Beach-fx analysis Planned Nourishment Planned nourishments are handled by the Beach-fx model as periodic events based on nourishment templates, triggers, and nourishment cycles. Nourishment templates are specified at the model reach level and include all relevant information such as order of fill, dimensions, placement rates, unit costs, and borrow-to-placement ratios. Planned nourishments occur when user defined nourishment triggers are exceeded and a mobilization threshold volume is met. At a pre-set interval, all model reaches which have been identified for planned nourishment are examined. In reaches where one of the nourishment threshold triggers is exceeded, the required volume to restore the design template is computed. If the summation of individual model reach level volumes exceeds the mobilization threshold volume established by the user, then nourishment is triggered and all model reaches identified for planned nourishment are restored to the nourishment template Nourishment Templates For Jupiter-Carlin, the Beach-fx nourishment template must reflect the existing federally authorized design template as well as the sacrificial volume that is traditionally referred to as Advance Fill. Based upon the project authorization, the design template consists of a zero foot berm extension at the 1990 MHW line. The advance fill volume at the time of initial construction was 513,000 cubic yards. Based on profile dimensions (and confirmed through average renourishment volumes from Beach-fx), this volume is equivalent to the 100 nourishment template (shown in Table A- 19). It is the purpose of the Section 934 analysis to determine if the authorized design template (the 1990 MHW line) plus the advance fill volume currently being placed (equivalent of the 100 nourishment template) remains economically justified. However, should the existing project no longer be justified due to changing environmental conditions, advance fill volumes can be optimized (under 934 Guidance). Therefore, additional Advance fill volumes were also evaluated in case such optimization would be required. Each Jupiter-Carlin nourishment template reflects the authorized zero-foot berm extension of the 1990 MHW line (authorized design template) plus a variable volume of advance fill. Table A- 19 summarizes the fill alternatives, including the initial berm width, the berm width required to complete the authorized design template (to 1990 MHW line), and the total template berm width (measured from the 2018 dune) that comprise each of the alternative templates. A-51

56 Table A- 17. Nourishment Templates Nourishment Distance Triggers and Mobilization Threshold Beach-fx planned nourishment templates have three nourishment distance triggers (1) berm width, (2) dune width, and (3) dune height. Each distance trigger is a fractional amount of the corresponding nourishment template dimension. When the template dimensions fall below the fraction specified by the trigger, a need for renourishment is indicated. For any project template, the berm width trigger can be set such that a minimum berm width (what has been traditionally referred to as a design berm ) can be maintained, allowing the remainder of the template to act as sacrificial fill (traditional advance fill ). The Jupiter-Carlin study alternatives each included a single maintained berm option (0-foot berm extension of the 1990 MHW line) and variable amounts of sacrificial fill. Because the width of the berm governs the alternatives, the dune width and dune height triggers were set to allow minimal erosion of the dune itself. For all cases that include a berm, the dune width and dune height triggers were set to 0.99 (1% loss of height allowed) and 0.90 (10% loss of height allowed), respectively. The mobilization threshold (minimum nourishment volume required to trigger a nourishment cycle) was set to be approximately the volume of the sacrificial portion of the nourishment template. This ensures that both the berm width trigger and mobilization threshold act together to maintain the desired design berm for each alternative. Distance Triggers and Mobilization thresholds for the Jupiter-Carlin project alternatives are presented in greater detail under Section 6.6: Beach-fx Project Design Alternatives. 6.6 Beach-fx Project Design Alternatives In order to fully evaluate the authorized as well as optimized alternative protective beach templates for Jupiter-Carlin, twelve alternatives were developed by combining the design reaches and nourishment templates discussed previously (Table A- 19). Additionally, for each template the authorized ( design ) berm width (as described in the previous section) was ensured through a combination of distance triggers and volume threshold values. Table A- 20 provides each of the project alternatives as well as corresponding berm distance triggers and design thresholds. As discussed previously, dune width and dune height distance triggers were set to 0.99 and 0.90, respectively for all alternatives. A-52

57 Table A- 18. Beach-fx Berm Distance Triggers and Threshold Volumes 6.7 Recommendation Beach-fx modeling and economic analysis determined that the existing project ( 100 Berm alternative) is not economically justified based on current guidelines and policies (see the Economics Appendix). However, analysis of the array of alternative templates showed that the 10 Berm alternative, when initially constructed from an offshore sand source and subsequently maintained by upland truck haul events, provides an economically justified means of maintaining the authorized project dimensions using a significantly lower volume of advance fill than has previously been placed. 7 Design Criteria Based on analysis and modeling efforts documented in the 1987 and 1994 GDMs, the present authorized plan for the Palm Beach County, Jupiter-Carlin Segment was formulated. Updated modeling and economic analysis have shown that while the present authorized design template and advanced fill volume is not justified, the authorized design template with a reduced volume of advanced fill is economically justified. A detailed description of the plan is presented in the following sections. 7.1 Project Length The authorized project consists of 1.1 miles of shoreline just south of Jupiter Inlet. The northern limit of the beachfill is located at FDEP monument R-13, approximately 500 feet south of the inlet s south jetty. A 700 foot taper starting at R-13 and extending to approximately R-13.7 connects the fill to the northern shoreline. The southern limit is located at R-19. A 1,200 foot taper between R-18 and R-19 connects the fill to the existing southern shoreline. 7.2 Project Baseline The project consists of a 0-foot extension of the 1990 mean high water (MHW) shoreline. Table A- 21 defines the location of the 1990 MHW shoreline relative to R-monuments within the project area. A-53

58 Table A- 19. Project Baseline Relative to R-monument Distance Relative R-monument to R-monument (ft) R R R R R R R Berm Elevation Based on the existing natural berm elevation, the authorized design berm was placed at +7.5 ft-navd Berm Widths Based on modeling and economic analysis described in the 1987 and 1994 GDMs, the authorized fill consists of a 0-foot extension of the project baseline (1990 MHW line) while providing additional material (traditionally referred to as Advance Fill ) to offset erosive losses over an estimated seven years between renourishments. Due to the layout of the shoreline and dune system, the authorized extension of the baseline results in actual fill berms widths (relative to the 1990 MHW line) ranging from 50 feet (R-17) to 210 feet (R-13). These variable berm widths are shown under the 10 template column in Table A Beach Slopes For Jupiter-Carlin, the native beach slope was estimated as 1 (vertical) on 10 (horizontal) above MLW and 1 on 25 below MLW. The construction slope was assumed to be 1 on Project Volumes and Renourishment Interval Shoreline response and economic analyses detailed in the 1994 GRR resulted in a project template that consisted of a 0-foot extension of a specified project baseline (1990 MHW line). The GRR estimated that initial construction would require approximately 701,000 cubic yards, followed by an additional 513,000 cubic yards of renourishment at seven year intervals. Table A- 20. Nourishment Template Variable Dune Widths A-54